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/*
Copyright (C) 2018 arbguest
This file is part of Arb.
Arb is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 2.1 of the License, or
(at your option) any later version. See <http://www.gnu.org/licenses/>.
*/
#include "acb_mat.h"
static void
_apply_permutation(slong * AP, acb_mat_t A, slong * P,
slong n, slong offset)
{
if (n != 0)
{
acb_ptr * Atmp;
slong * APtmp;
slong i;
Atmp = flint_malloc(sizeof(acb_ptr) * n);
APtmp = flint_malloc(sizeof(slong) * n);
for (i = 0; i < n; i++) Atmp[i] = A->rows[P[i] + offset];
for (i = 0; i < n; i++) A->rows[i + offset] = Atmp[i];
for (i = 0; i < n; i++) APtmp[i] = AP[P[i] + offset];
for (i = 0; i < n; i++) AP[i + offset] = APtmp[i];
flint_free(Atmp);
flint_free(APtmp);
}
}
static void
_acb_approx_mul(acb_t res, const acb_t x, const acb_t y, slong prec)
{
arf_complex_mul(arb_midref(acb_realref(res)), arb_midref(acb_imagref(res)),
arb_midref(acb_realref(x)), arb_midref(acb_imagref(x)),
arb_midref(acb_realref(y)), arb_midref(acb_imagref(y)), prec, ARB_RND);
}
static void
_acb_approx_inv(acb_t z, const acb_t x, slong prec)
{
arf_set(arb_midref(acb_realref(z)), arb_midref(acb_realref(x)));
arf_set(arb_midref(acb_imagref(z)), arb_midref(acb_imagref(x)));
mag_zero(arb_radref(acb_realref(z)));
mag_zero(arb_radref(acb_imagref(z)));
acb_inv(z, z, prec);
mag_zero(arb_radref(acb_realref(z)));
mag_zero(arb_radref(acb_imagref(z)));
}
static void
_acb_vec_approx_scalar_addmul(acb_ptr res, acb_srcptr vec,
slong len, const acb_t c, slong prec)
{
acb_t t;
slong i;
acb_init(t);
for (i = 0; i < len; i++)
{
_acb_approx_mul(t, vec + i, c, prec);
arf_add(arb_midref(acb_realref(res + i)),
arb_midref(acb_realref(res + i)),
arb_midref(acb_realref(t)), prec, ARB_RND);
arf_add(arb_midref(acb_imagref(res + i)),
arb_midref(acb_imagref(res + i)),
arb_midref(acb_imagref(t)), prec, ARB_RND);
}
acb_clear(t);
}
int
acb_mat_approx_lu_classical(slong * P, acb_mat_t LU, const acb_mat_t A, slong prec)
{
acb_t d, e;
acb_ptr * a;
slong i, j, m, n, r, row, col;
int result;
if (acb_mat_is_empty(A))
return 1;
m = acb_mat_nrows(A);
n = acb_mat_ncols(A);
acb_mat_get_mid(LU, A);
a = LU->rows;
row = col = 0;
for (i = 0; i < m; i++)
P[i] = i;
acb_init(d);
acb_init(e);
result = 1;
while (row < m && col < n)
{
r = acb_mat_find_pivot_partial(LU, row, m, col);
if (r == -1)
{
result = 0;
break;
}
else if (r != row)
acb_mat_swap_rows(LU, P, row, r);
_acb_approx_inv(d, a[row] + col, prec);
for (j = row + 1; j < m; j++)
{
_acb_approx_mul(e, a[j] + col, d, prec);
acb_neg(e, e);
_acb_vec_approx_scalar_addmul(a[j] + col,
a[row] + col, n - col, e, prec);
acb_zero(a[j] + col);
acb_neg(a[j] + row, e);
}
row++;
col++;
}
acb_clear(d);
acb_clear(e);
return result;
}
int
acb_mat_approx_lu_recursive(slong * P, acb_mat_t LU, const acb_mat_t A, slong prec)
{
slong i, m, n, r1, r2, n1;
acb_mat_t A0, A1, A00, A01, A10, A11;
slong * P1;
m = A->r;
n = A->c;
if (m <= 1 || n <= 1)
{
return acb_mat_approx_lu_classical(P, LU, A, prec);
}
acb_mat_get_mid(LU, A);
n1 = n / 2;
for (i = 0; i < m; i++)
P[i] = i;
P1 = flint_malloc(sizeof(slong) * m);
acb_mat_window_init(A0, LU, 0, 0, m, n1);
acb_mat_window_init(A1, LU, 0, n1, m, n);
r1 = acb_mat_approx_lu(P1, A0, A0, prec);
if (!r1)
{
flint_free(P1);
acb_mat_window_clear(A0);
acb_mat_window_clear(A1);
return 0;
}
/* r1 = rank of A0 */
r1 = FLINT_MIN(m, n1);
_apply_permutation(P, LU, P1, m, 0);
acb_mat_window_init(A00, LU, 0, 0, r1, r1);
acb_mat_window_init(A10, LU, r1, 0, m, r1);
acb_mat_window_init(A01, LU, 0, n1, r1, n);
acb_mat_window_init(A11, LU, r1, n1, m, n);
acb_mat_approx_solve_tril(A01, A00, A01, 1, prec);
{
/* acb_mat_submul(A11, A11, A10, A01, prec); */
acb_mat_t T;
acb_mat_init(T, A10->r, A01->c);
acb_mat_approx_mul(T, A10, A01, prec);
acb_mat_sub(A11, A11, T, prec);
acb_mat_get_mid(A11, A11);
acb_mat_clear(T);
}
r2 = acb_mat_approx_lu(P1, A11, A11, prec);
if (!r2)
r1 = r2 = 0;
else
_apply_permutation(P, LU, P1, m - r1, r1);
flint_free(P1);
acb_mat_window_clear(A00);
acb_mat_window_clear(A01);
acb_mat_window_clear(A10);
acb_mat_window_clear(A11);
acb_mat_window_clear(A0);
acb_mat_window_clear(A1);
return r1 && r2;
}
int
acb_mat_approx_lu(slong * P, acb_mat_t LU, const acb_mat_t A, slong prec)
{
if (acb_mat_nrows(A) < 8 || acb_mat_ncols(A) < 8)
return acb_mat_approx_lu_classical(P, LU, A, prec);
else
return acb_mat_approx_lu_recursive(P, LU, A, prec);
}
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